Question

1. Suppose scientists were researching a fox having white fur in a large number of foxes. For the individual fox, suppose that the probability a fox has white fur is 25%.
   1. What is the probability that at most 4 foxes need to be researched until the first fox with white fur is found?
   2. What is the probability that at most 4 foxes need to be researched until the third fox with white fur is found?

Answer 1

a) Let X denotes the number of foxes need to be researched until the first fox with white fur is found.

X ~ Geometric(p = 0.25)

The probability mass function of X is

Now,

The probability that at most 4 foxes need to be researched until the first fox with white fur is found

b) Let Y denotes the number of foxes need to be researched until the third fox with white fur is found.

Y ~ Negative Binomial(r = 3, p = 0.25)

The probability mass function of Y is

Now,

The probability that at most 4 foxes need to be researched until the third fox with white fur is found